each function is either even or odd .use f(-x) to state which situation applies f(x)=5x^3-8x please help

Question

anonymous · Answer

do you get the difference between even and odd functions?

anonymous · Answer

This is a good resource to start with: http://www.purplemath.com/modules/fcnnot3.htm Feel free to ask if you still have any questions

unklerhaukus · Answer

Find f(-x) :

anonymous · Answer

i will look at it thank you

unklerhaukus · Answer

$$f(x)=5x^3-8x$$
so
$$f(-x)=5(-x)^3-8(-x)$$
.. can you simplify this?

anonymous · Answer

-5x^3+8x

unklerhaukus · Answer

good, so you found $$f(-x)=-5x^3+8x$$

if we now factor out the negative sign$$f(-x)=-(5x^3-8x)$$

We have the negative of the original function$$f(-x)=-f(x)$$

This is the definition of an odd function.

anonymous · Answer

thank you :)

unklerhaukus · Answer

if we had gotten$$f(-x) = f(x)$$, (after simplification), it would have been an even function